/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Express each interval in set-bui... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 11

Express each interval in set-builder notation and graph the interval on a number line. $$(-\infty, 3)$$

Short Answer

Expert verified
In set-builder notation, the interval \(-\infty, 3)\ is \(x: x < 3\). The graph would be a hollow circle at 3, with a line extending to the left towards \(-\infty\).

Step by step solution

01

Interpret the Open Intervals

Open intervals are given by \((a, b)\), where \(a\) and \(b\) are the endpoints. If \(a\) or \(b\) is replaced by \(-\infty\), that means all numbers going towards negative infinity are included. For this exercise, \(-\infty\) corresponds to the lower limit, while 3 corresponds to the upper limit. It is open at 3, means all the numbers less than 3 are considered here. None of the end points are included, it is denoted by hollow circles.
02

Convert to Set-Builder Notation

Set-builder notation is another way to denote intervals. For \(-\infty, 3)\, all numbers less than 3 are included. This can expressed in set-builder notation as: \(x: x < 3\), where 'x' is the element of the set.
03

Graph the Interval on a Number Line

Draw a number line and mark the point corresponding to 3. Since the interval is open at 3, indicate this with a hollow circle at 3. Draw a line starting from 3 and extending to the left towards \(-\infty\). This represents all numbers less than 3.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$V=\frac{1}{3} B h \text { for } B$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$I R+I r=E \text { for } I$$

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure at the top of the next column. If the area of the pool and the path combined is 600 square meters, what is the width of the path?

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$C=2 \pi r \text { for } r$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.